Final answer:
Vector A is (5i - 5j + 3k) and Vector B is (0i + 2j - 1k). The values for a, b, 2a-3b, |a|, and |a-b| are calculated.
Step-by-step explanation:
Vector A and Vector B
A = 5i - 5j + 3k
B = 0i + 2j - 1k
Find a, b, 2a-3b, |a|, and |a-b|
a = 5i - 5j + 3k
b = 0i + 2j - 1k
2a - 3b = 2(5i - 5j + 3k) - 3(0i + 2j - 1k) = 10i - 10j + 6k - 0i - 6j + 3k = 10i - 16j + 9k
|a| = sqrt((5^2) + (-5^2) + (3^2)) = sqrt(75) = 5sqrt(3)
|a-b| = sqrt((5-0)^2 + (-5-2)^2 + (3-(-1))^2) = sqrt(70)